Find the length of the c side of the mathrm Del... - SS2 Mathematics Trigonometric Ratios II Question
Find the length of the c side of the \(\mathrm{\Delta}ABC\) which have \(a = 5.3cm,\ b = 8.9cm\ \)and\(\ \angle C = 55{^\circ}\) using the cosine rule
A
5.9cm
B
7.3cm
C
6.7cm
D
8.8cm
correct option: b
Using the cosine rule, \(c^{2} = a^{2} + b^{2} - 2ab\cos C\)
\[c^{2} = {5.3}^{2} + {8.9}^{2} - 2(5.3)(8.9)\cos 55\]
\[c^{2} = 28.09 + 79.21 - 2(5.3)(8.9)(0.5736)\]
\[c^{2} = 28.09 + 79.21 - 54.11\]
\(c = \sqrt{53.19} = 7.3cm\)
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